What is the electrochemical equivalence of Faraday's first law?
2 Answers
Faraday's first law of electrolysis states that the amount of substance transformed during electrolysis is directly proportional to the quantity of electric charge passed through the electrolyte. The electrochemical equivalence can be expressed mathematically as:
\[ m = \frac{Q}{F} \cdot \frac{M}{n} \]
where:
- \( m \) is the mass of the substance deposited or dissolved,
- \( Q \) is the total electric charge (in coulombs),
- \( F \) is Faraday's constant (approximately 96485 C/mol, representing the charge of one mole of electrons),
- \( M \) is the molar mass of the substance,
- \( n \) is the number of moles of electrons exchanged per mole of the substance in the reaction.
This equation illustrates how the mass of a substance is related to the amount of electric charge and the stoichiometry of the redox reaction occurring during electrolysis.
\[ m = \frac{Q}{F} \cdot \frac{M}{n} \]
where:
- \( m \) is the mass of the substance deposited or dissolved,
- \( Q \) is the total electric charge (in coulombs),
- \( F \) is Faraday's constant (approximately 96485 C/mol, representing the charge of one mole of electrons),
- \( M \) is the molar mass of the substance,
- \( n \) is the number of moles of electrons exchanged per mole of the substance in the reaction.
This equation illustrates how the mass of a substance is related to the amount of electric charge and the stoichiometry of the redox reaction occurring during electrolysis.
Faraday's first law of electrolysis states that the amount of substance transformed during electrolysis is directly proportional to the quantity of electricity passed through the electrolyte. This can be mathematically expressed using the concept of electrochemical equivalence.
**Electrochemical Equivalence**: The electrochemical equivalence of a substance refers to the amount of that substance that is deposited or dissolved per unit charge passed through an electrolyte. It provides a way to quantify how much of a substance will be transformed in an electrochemical reaction.
**Mathematically**, the electrochemical equivalence (E) can be defined as:
\[ E = \frac{m}{Q} \]
where:
- \( m \) is the mass of the substance deposited or dissolved,
- \( Q \) is the quantity of electricity (charge) passed through the electrolyte.
**Faraday's First Law** in terms of electrochemical equivalence can be expressed as:
\[ m = E \times Q \]
where:
- \( m \) is the mass of the substance transformed,
- \( E \) is the electrochemical equivalence of the substance,
- \( Q \) is the total charge passed through the electrolyte.
To find the electrochemical equivalence \( E \), you can use:
\[ E = \frac{m}{Q} = \frac{M}{nF} \]
where:
- \( M \) is the molar mass of the substance,
- \( n \) is the number of moles of electrons required to transform one mole of the substance (from the balanced chemical reaction),
- \( F \) is Faraday's constant (approximately 96485 C/mol), which represents the charge of one mole of electrons.
**Example**:
If you want to determine how much silver is deposited when a current of 2 amperes is passed through a solution of silver nitrate for 1 hour, you need to know the electrochemical equivalence of silver.
1. **Find the charge (Q)**:
\[ Q = \text{Current} \times \text{Time} \]
\[ Q = 2 \, \text{A} \times 3600 \, \text{s} = 7200 \, \text{C} \]
2. **Find the electrochemical equivalence (E)**:
For silver (Ag), the molar mass \( M \) is approximately 107.87 g/mol, and it requires 1 mole of electrons to deposit 1 mole of silver (n = 1).
Thus,
\[ E = \frac{M}{nF} = \frac{107.87 \, \text{g/mol}}{96485 \, \text{C/mol}} \approx 0.00112 \, \text{g/C} \]
3. **Calculate the mass (m)**:
\[ m = E \times Q \]
\[ m = 0.00112 \, \text{g/C} \times 7200 \, \text{C} \approx 8.06 \, \text{g} \]
So, about 8.06 grams of silver would be deposited.
In summary, Faraday's first law relates the quantity of a substance transformed to the quantity of electricity used, and electrochemical equivalence provides a way to quantify this relationship.
**Electrochemical Equivalence**: The electrochemical equivalence of a substance refers to the amount of that substance that is deposited or dissolved per unit charge passed through an electrolyte. It provides a way to quantify how much of a substance will be transformed in an electrochemical reaction.
**Mathematically**, the electrochemical equivalence (E) can be defined as:
\[ E = \frac{m}{Q} \]
where:
- \( m \) is the mass of the substance deposited or dissolved,
- \( Q \) is the quantity of electricity (charge) passed through the electrolyte.
**Faraday's First Law** in terms of electrochemical equivalence can be expressed as:
\[ m = E \times Q \]
where:
- \( m \) is the mass of the substance transformed,
- \( E \) is the electrochemical equivalence of the substance,
- \( Q \) is the total charge passed through the electrolyte.
To find the electrochemical equivalence \( E \), you can use:
\[ E = \frac{m}{Q} = \frac{M}{nF} \]
where:
- \( M \) is the molar mass of the substance,
- \( n \) is the number of moles of electrons required to transform one mole of the substance (from the balanced chemical reaction),
- \( F \) is Faraday's constant (approximately 96485 C/mol), which represents the charge of one mole of electrons.
**Example**:
If you want to determine how much silver is deposited when a current of 2 amperes is passed through a solution of silver nitrate for 1 hour, you need to know the electrochemical equivalence of silver.
1. **Find the charge (Q)**:
\[ Q = \text{Current} \times \text{Time} \]
\[ Q = 2 \, \text{A} \times 3600 \, \text{s} = 7200 \, \text{C} \]
2. **Find the electrochemical equivalence (E)**:
For silver (Ag), the molar mass \( M \) is approximately 107.87 g/mol, and it requires 1 mole of electrons to deposit 1 mole of silver (n = 1).
Thus,
\[ E = \frac{M}{nF} = \frac{107.87 \, \text{g/mol}}{96485 \, \text{C/mol}} \approx 0.00112 \, \text{g/C} \]
3. **Calculate the mass (m)**:
\[ m = E \times Q \]
\[ m = 0.00112 \, \text{g/C} \times 7200 \, \text{C} \approx 8.06 \, \text{g} \]
So, about 8.06 grams of silver would be deposited.
In summary, Faraday's first law relates the quantity of a substance transformed to the quantity of electricity used, and electrochemical equivalence provides a way to quantify this relationship.